Numerical Investigation Of Several Difference Schemes For Brusselator System

Brusselator system is an important model in chemistry,physics and control discipline.It is widely used to describe chemical reactions,fluid mechanics and oscillatory circuits.In view of the special structure of the semi-discrete equation,implicit-explicit methods are introduced to solve the problem.And convergence and stability of the schemes are investigated.In Chapter 1,the background of the Brusselator reaction diffusion model and the numerical schemes of partial differential equations are introduced.The structure of the study is given.In Chapter 2,some implicit-explicit Euler difference schemes and their applications are given.Then,the implicit-explicit Euler center difference scheme is applied to approximate the Brusselator system.The stability and convergence of the difference schemes are proved by using mathematical induction and Gronwall inequality.Numerical examples are given to verify the convergence of the schemes.Then,the compact difference schemes are used to discrete the diffusion term.And the implicit-explicit scheme is applied to approximate the resulting system.The convergence and stability of the difference schemes are also proved.In Chapter 3,some linearized Crank-Nicolson schemes and their applications are given.Then,the linearized Crank-Nicolson center difference scheme is applied to approximate the Brusselator system.The convergence of the difference schemes are proved by using mathematical induction and Gronwall inequality.Numerical examples are given to verify the convergence of the schemes.Then,the compact difference schemes are used to discrete the diffusion term.And the implicit-explicit scheme is applied to approximate the resulting system.The convergence of the difference schemes are also proved.In Chapter 4,conclusions and discussions are presented.